Curvature-Aligned Subdivision Surface Generation from Faceted Geometry
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Solution Overview
Problem
Existing CAD software requires manual creation of subdivision surfaces from faceted geometry, which is inefficient and lacks automatic curvature alignment, necessitating a method to generate smooth surfaces that accurately represent input geometry with minimal patches.
Innovation Solution
The method involves generating a curvature-aligned cross field on a triangular mesh to calculate a quad layout forming the control cage of a subdivision surface, with iterative refinement and vertex insertion to achieve a desired approximation tolerance, using the Catmull-Clark subdivision scheme.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If manual creation of subdivision surfaces is used, then the control cage can be precisely defined, but the process is inefficient and time-consuming
Solution Approach 1:
The system performs automatic curvature analysis and quad layout generation without requiring manual user input. The algorithm independently computes curvature-aligned cross fields and generates the control cage structure automatically, allowing the software to serve itself rather than requiring continuous user intervention
Solution Approach 2:
The system transforms the input triangular mesh by computing curvature parameters at each vertex and using these parameters to determine the optimal quad layout. By changing from manual vertex placement to automated parameter-driven layout, the system achieves both efficiency and quality
2Manufacturing precision
If curvature alignment is not considered, then the surface generation is simpler, but the number of patches increases and accuracy decreases
Solution Approach 1:
The system performs curvature analysis and cross field computation before generating the final subdivision surface. By pre-computing the curvature-aligned layout, the system ensures optimal patch distribution from the start, avoiding the need for subsequent refinement and reducing the total number of patches required
Solution Approach 2:
The system computes curvature-specific properties at each vertex location and uses these local properties to determine the quad layout. Each region of the surface is treated differently based on its local curvature characteristics, ensuring high accuracy in representing both high-curvature and low-curvature areas
3Productivity
If the number of patches is reduced, then the surface is more efficient, but it becomes harder to achieve accurate representation of complex geometry
Solution Approach 1:
The system uses curvature information to guide the placement and orientation of quad patches across the surface. By aligning the grid structure with the principal curvature directions, the system achieves accurate representation of complex geometry using fewer patches, as each patch better conforms to the underlying surface shape
Data Source
AI summary
Data is received that includes a triangular mesh. Thereafter, a curvature aligned cross field is generated on the triangular mesh. The cross field is used to calculate a quad layout. A subdivision surface can be created using the quad layout as a control cage. Later, vertex locations in the control cage are determined to result in the subdivision surface being an approximation of the triangular mesh. The subdivision subsurface (or a portion thereof) can be visualized in a graphical user interface (e.g., as part of a CAD software application, etc.). Related apparatus, systems, techniques and articles are also described.